If the Sun (or a star) is in hydrostatic equilibrium, the Sun (or star)
is neither expanding nor contracting; it is sitting nicely in some
equilibrium configuration. This means that the forces which control the
Sun (or star) are precisely balanced.
For the Sun (and stars):
If the temperature structure of the Sun (or a star) is not changing with time,
then the Sun (or star) is in
Thermal Equilbrium. This will happen if the
energy production exactly balances the energy losses of the Sun (or star).
For the Sun, since
The important question of the energy source of the Sun is a longstanding one which was not answered satisfactorily until the twentieth century. We now discuss
An important test of our ideas (as discussed earlier) concerns the detection of the ghostlike particles know as neutrinos. This important experiment showed that we have a good understanding of the Sun. As a major benefit, it also expanded our understanding of the properties of neutrinos, some of the fundamental particles which make up our Universe. For the more technically minded, the late John Bahcall's website www.sns.ias.edu/~jnb contains a very good discussion of Solar neutrinos and the Solar model.
Solar oscillations are another sensitive probe of the interior of the Sun. Go to the website http://gong.nso.edu/info to find more information on the Global Oscillation Network Group, GONG.
The Sun is like a bell in that if you kick it, it rings. The source that excites the most of the observed Solar oscillations, is the convective layer and so, the Sun is like a bell that is continuously buffetted by many small kicks. The GONG experiment detects and studies the different ways in which the Sun rings. The exact manner in which the Sun rings is determined by the details of its interior structure (in particular, by the details of the convection layer). So, studying the way in which the Sun rings gives us another way to study what the Sun looks like beneath its surface. (The technique is similar to that used by geologists who use seismology to study the interior of the Earth. For the Sun, the science is called helioseismology.)
The Sun rings in many different ways depending on the details of the interior of the Sun, the sound waves bounce around and travel through the Sun in different ways and with different speeds. Some rattle around near the surface of the Sun, some are trapped in the convective layer of the Sun, and some stretch to the center of the Sun. (The motions generate sound waves -- The Boiling and Singing Sun.)
Scientists model these waves finding things which look like (the "cells" represent where the waves bounce off the surface of the Sun, and so on [see the above picture and the picture below]).
The following mpeg movie show solar oscillations.
The current GONG results (depend on the sound wave speeds [the sound speed] and other aspects of the ringing) compare well to the predictions made by current Solar models. The GONG site's K-3 link is a little low-level, but is amusing.